Admixture mass transfer is studied in geometrically complex systems. The method is proposed for finding an exact solution of initial-boundary value problem of diffusion in bodies with two-phase periodical structure. It is based on application of integral transformations with respect to space variables in contacting areas. The behaviour of mass transfer processes in such systems is investigated. The relation between problems of mass transfer in horizontally periodical structure and heterodiffusion by two ways is found. (c) 2005 Elsevier Ltd. All rights reserved.